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8/14/2019 First Law Thermo
1/27
Thermodynamics M. D. Eastin
First Law of Thermodynamics
ValveOpen
AirAir
What energy
transformations occur as
air parcels move around
within thunderstorms?
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Thermodynamics M. D. Eastin
Outline:
Forms of Energy
Energy Conservation
Concept of Work
PV DiagramsConcept of Internal Energy
Joules Law
Thermal Capacities (Specific Heats)
Concept of Enthalpy
Various Forms of the First Law
Types of Processes
First Law of Thermodynamics
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Thermodynamics M. D. Eastin
Forms of Energy
Energy comes in a variety of forms
Potential
Mechanical Chemical Electrical
Internal Kinetic
Heat
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Thermodynamics M. D. Eastin
Energy Conservation
The First Law of Thermodynamicsstates that total energy is conserved for any
thermodynamic system energy can not be created nor destroyed energy can only change from one form to another
constant)( EEnergy
constantelectricalchemicalheat
mechanicalpotentialkineticinternal
EEE
EEEE
Our main concern in meteorology
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Thermodynamics M. D. Eastin
The Concept of Work
Workis a Mechanicalform of Energy:
DistanceForceWork
xFdW
Force
Distance
x
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Thermodynamics M. D. Eastin
The Concept of Work
Workis a Mechanicalform of Energy:
Recall the definition of pressure:
We can thus define work as:
DistanceForceWork
xFdW
2AreaForce
px
F
pdVdW
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The Concept of Work
Changes in Volume Cause Work:
Work is performed when air expands
Work of Expansion:
Occurs when a system performs work
(or exerts a force) on its environment
Is positive:
Rising air parcels (or balloons) undergo expansion work
Since the environmental pressure decreases with height,
with height a rising parcel must expand
to maintain an equivalent pressure
0dW
F
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The Concept of Work
Changes in Volume Cause Work:
Similar to a piston in a car engine
FF
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The Concept of Work
Changes in Volume Cause Work:
Work is performed when air contracts
Work of Contraction:
Occurs when an environment performs work
(or exerts a force) on a system
Is negative:
Sinking air parcels (or balloons) undergo contraction work
Since the environmental pressure decreases with height,
with height a sinking parcel must contract
to maintain an equivalent pressure
0dW
FF
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Pressure-Volume (PV) Diagrams
Another Way of Depicting Thermodynamic Processes:
Consider the transformation: i f
p
VVfVi
pi
pf
i
f
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Another Way of Depicting Work:
Consider the transformation: i f
p
V
pdVdW
f
ipdVW
VfVi
pi
pf
i
f The work done is the area
under the i f curve
(or gray area)
Pressure-Volume (PV) Diagrams
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Internal Energy= Kinetic Energy +Potential Energy
(of the molecules in the system)Depends onlyon the current system state (p,V,T)Does notdepend on past statesDoes notdepend on how state changes occur
Changes are the result of external forcingon the system (in the form of workor heat)
First Law of Thermodynamics
tenvironmentenvironmeninternal HeatWorkE
dQdWdU
dQpdVdU
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Joules Law
Valve
Closed
AirVacuum
Thermally Insulated System
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Joules Law
Thermally Insulated System
Valve
Open
AirAir
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Joules Law
dQpdVdU
Valve
Open
AirAir
Air expanded to fill the container
Change in volumeChange in pressure
No external work was done
Air expanded into a vacuum
within the system
No heat was added or subtract
Thermally insulated system
No change in internal energy
No change in temperature
What does this mean?
0dU
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Joules Law
dQpdVdU
Valve
Open
AirAir
Air expanded to fill the container
Change in volumeChange in pressure
No external work was done
Air expanded into a vacuum
within the system
No heat was added or subtract
Thermally insulated system
No change in internal energy
No change in temperature
Internal Energy is only a function oftemperature
0dU U(T)U
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Thermal Capacities (Specific Heats)
Assume: A small quantity of heat (dQ) is given to a parcel
The parcel responds by experiencing a small temperature increase (dT)
Specific Heat (c):
Two Types of Specific Heats:
Depends on how the material changes as it receives the heat
Constant Volume:
Constant Pressure:
volumeconstant
vdT
dQc
Parcel experiences no
change in volume
Parcel experiences no
change in pressure
pressureconstant
pdT
dQc
dT
dQc
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Thermal Capacities (Specific Heats)
Specific Heat at Constant Volume:
Starting with:
If the volume is constant (dV = 0), we can re-write the first law as:
And substitute this into our specific heat equation as
volumeconstant
vdT
dQc
dQpdVdU dQdU
dT
dUcv or dTcdU v
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Thermal Capacities (Specific Heats)
Specific Heat at Constant Volume:
Since the internal energy is a state variable and does not depend on past statesor how state changes occur, we can define changes in internal energy as:
Also, if we substitute our specific heat equation into the first law:
We can obtain an alternative formof the First Law of Thermodynamics:
2
2
dTcU vT
T
pdVdTcdQ v
dQpdVdU dTcdU v
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Thermal Capacities (Specific Heats)
Specific Heat at Constant Pressure:
Starting with
and recognizing that,
we can obtain another alternative formof the First Law of Thermodynamics:
Also,
pressureconstant
pdT
dQc
pdVdTcdQ v
VdppdVd(pV)
VdpdTcdQ p
*
vp nRcc
TnRpV *
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Concept of Enthalpy
Assume: Heat (dQ) is added to a system at constant pressure
Impact: 1) The systems volume increases (V1V2) and work is done
2) The systems internal energy increases (U1U2)
Using the First Law:
We can then define Enthalpy (H)as:
)V-p(VdW 12
12 U-UdU
1212
VVpUUdQ
pVUH
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Thermodynamics M. D. Eastin
Concept of Enthalpy
Enthalpy:
If we differentiate the definition of enthalpy and use prior relationships, we can
obtain the following relation:
We shall see that Enthalpywill be a useful concept since most sources and
sinks of heating in the atmosphere occur at roughly constant pressure
1212 VVpUUdQ
pVUH
dTcdHdQ p
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Thermodynamics M. D. Eastin
Forms of the First Law of Thermodynamics
For a gas of mass m For unit mass
dWdUdQ pdVdUdQ
pdVdTcdQ v
VdpdTcdQ p
dwdudq pddudq
pddTcdq v
dpdTcdq p
where: p = pressure U = internal energy
V = volume W = work
T = temperature Q = heat energy
= specific volume n = number of moles
cv= specific heat at constant volume (717 J kg-1K-1)
cp= specific heat at constant pressure (1004 J kg-1K-1)
Rd= gas constant for dry air (287 J kg-1K-1)
R* = universal gas constant (8.3143 J K-1mol-1)
nRcc *vp Rcc dvp
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Thermodynamics M. D. Eastin
Types of Processes
Isobaric Processes:
Transformations at constant pressuredp = 0
Isochoric Processes:
Transformations at constant volume
dV = 0d= 0
p
V
i f
p
V
i
f
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Thermodynamics M. D. Eastin
Types of Processes
Isothermal Processes:
Transformations at constant temperaturedT = 0
Adiabatic Processes:
Transformations without the exchange of heat
between the environment and the systemdQ = 0
More on this next lecture
p
V
i
f
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Thermodynamics M. D. Eastin
Summary:
Forms of Energy (know the seven types)Energy Conservation (know the basic concept)
Concept of Work (expansion and contraction in the atmosphere)
PV Diagrams (origins of an equation for Work)
Concept of Internal Energy (know the basic concept)
Joules Law (know what it implies to internal energy)
Thermal Capacities (Specific Heats)
Concept of Enthalpy (know the basic concept)
Various Forms of the First Law
Types of Processes (isobaric, isothermal, isochoric, adiabatic)
First Law of Thermodynamics
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References
Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp.
Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp.
Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp.
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